A351930 Expansion of e.g.f. exp(x - x^4/24).
1, 1, 1, 1, 0, -4, -14, -34, -34, 190, 1366, 5446, 11056, -30744, -421420, -2403764, -7434244, 9782396, 296347996, 2257819420, 9461601856, -1690329584, -395833164264, -3872875071064, -20629371958040, -17208144880024, 893208132927176, 10962683317693576
Offset: 0
Keywords
Programs
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Maple
a:= proc(n) option remember; `if`(n=0, 1, `if`(n<4, 0, -a(n-4)*binomial(n-1, 3))+a(n-1)) end: seq(a(n), n=0..27); # Alois P. Heinz, Feb 26 2022 -
PARI
my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(x-x^4/4!))) -
PARI
a(n) = n!*sum(k=0, n\4, (-1/4!)^k*binomial(n-3*k, k)/(n-3*k)!);
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PARI
a(n) = if(n<4, 1, a(n-1)-binomial(n-1, 3)*a(n-4));
Formula
a(n) = n! * Sum_{k=0..floor(n/4)} (-1/24)^k * binomial(n-3*k,k)/(n-3*k)!.
D-finite with recurrence a(n) = a(n-1) - binomial(n-1,3) * a(n-4) for n > 3.